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arXiv · 2012.11069

Anosov-Katok constructions for quasi-periodic $\mathrm{SL}(2,R)$ cocycles

Nikolaos Karaliolios·Xu Xu·Qi Zhou
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Abstract

We prove that if the frequency of the quasi-periodic $\mathrm{SL}(2,\R)$ cocycle is Diophantine, then the following properties are dense in the subcritical regime: for any $\frac{1}{2}<\kappa<1$, the Lyapunov exponent is exactly $\kappa$-H\"older continuous; the extended eigenstates of the potential have optimal sub-linear growth; and the dual operator associated a subcritical potential has power-law decay eigenfunctions. The proof is based on fibered Anosov-Katok constructions for quasi-periodic $\mathrm{SL}(2,\R)$ cocycles.

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Nikolaos Karaliolios, Xu Xu, Qi Zhou. 2020-12-21. Anosov-Katok constructions for quasi-periodic $\mathrm{SL}(2,R)$ cocycles. https://arxiv.org/abs/2012.11069

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